Implementing Secure multi-party computation for online website

Question

I need to know if the following is feasible: I want that any two users of my website have a private key such that the private key is divided into three parts one for website owner and one each for the two users.

I understand that the private key can be divided into 3 parts such that two of them can generate the full key using "Shamir's Secret Sharing" , however I want to know if it is possible to independently generate and distribute the key parts to each party, so that the users do not need to fear that the website or other user may have the private key.

I think it may be possible using multi-party computation but could not find any such implementation.

Thanks

Answer 1

What exactly constitutes the "private key"?

If the key is the private part of an asymmetric encryption key pair, such as for RSA, and you'd hence also like all three parties to know the public key, then what you're looking for is called distributed key generation. You can then also use threshold cryptography and let the parties compute private key operations – decryption and signatures – without any single party needing to have access to the full key.

If the key is any random string of bits (e.g. the key for a symmetric block cipher), and you want a secret sharing of this random value, what you want is called correlated randomness (see e.g. this paper by Ishai et al. from 2013 for its uses in multiparty computation). In this 2-out-of-3 case, you can simply let each party $i \in \{1, 2, 3\}$ generate a random $k$-bit string $r_i$ and send their value to the "next" party (i.e. party $i$ sends $r_i$ to party $i+1 \bmod3$). Define $r = r_1 \oplus r_2 \oplus r_3$ to be your random key. Then any single party has only two of the values $r_i$, and hence does not obtain any information about $r$, but any two parties can reconstruct $r$.